   Chapter 13.4, Problem 18E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# In Problems 17-26, p and C are in dollars and x is the number of units.The demand function for a product is p =   100   − 4 x . If the equilibrium price is \$40 per unit, what is the consumer’s surplus?

To determine

To calculate: The Consumer’s Surplus for a product whose demand function is approximated by p=1004x dollars. Where, the equilibrium price is 40 dollars per unit.

Explanation

Given Information:

Demand function is approximated by p=1004x dollars.

The equilibrium price is 40 dollars per unit.

Formula used:

According to the Consumer’s Surplus:

If the demand curve has equation p=f(x), the consumer surplus is given by the area between f(x) and the x axis from 0 to x1, less the area of TR is:

CS=0x1f(x)dxp1x1.

Calculation:

Consider the demand function,

p=1004x

Since, to know the quantity to be purchased at equilibrium price,

Let, p=40

Now, substitute the value p=40 in the demand function to get x1,

40=1004x4x=10040x=604x=15

Thus, the equilibrium point (x1,p1) can determine as,

x1=15p1=40

Consider the formula,

CS=</

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